FLINT3.7.0-dev
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arb_atan, arb_atan_arf

Synopsis#include <flint/arb.h>
void arb_atan(arb_t z, const arb_t x, slong prec)source
void arb_atan_arf(arb_t z, const arf_t x, slong prec)source

Set z to atan⁡x\operatorname{atan} x.

arb_atan computes the arctangent of the midpoint with arb_atan_arf and adds the propagated error, bounded by r/(1+(∣m∣−r)2)r / (1 + (|m| - r)^2) for r<∣m∣r < |m| and by min⁡(π,r)\min(\pi, r) in general; inaccurate input is evaluated at the endpoints. arb_atan_arf uses tables and a Taylor series below 3400 bits and a Newton iteration on arb_sin_cos above; the bit-burst algorithm arb_atan_arf_bb is the fallback when the tables are not precise enough.

Guides#

Cite this page

The FLINT team, “arb_atan, arb_atan_arf (arb.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb/arb_atan.html (generated 2026-11-02).